Test circuit for piezoelectric crystals



s sheets-sheet 1 FIG. 3

C. W. HARRISON TEST CIRCUIT FOR PIEZOELECTRIG CRYSTALS XL'A- CAL.

ATTORNEY PIEDRA CA* March 8, 1949.

Filed Feb. 7, 1945 FREQUENC? IND/CA TOR 'March s, 1949.

Filed Feb. 7, 1945 A FEEDBK C. W. HARRISON TEST CIRCUIT FOR PIEZOELECTRIC CRYSTALS 3 Sheets-Sheet 2 /N VEN TOR Ic. w HAM/50N ATTORNEY c. w. HARRlsoN 2,463,616 TEST CIRCUIT FOR PIEZOELECTRIC CRYSTALS 3 Sheets-$heet 3 u, 7% ha N@ n RJ 11.11 ful 4:. I LU lll 1| Dhr W I:

March 8, 1949.

Filed Feb. 7, 1945 INVENTUR By cw HARR/so/v wat 7M. 7&6@

ATTORNEY Patented Mar. 8,1949

OFFICE 'l'lST CIIUUIT FOB mmc CIYBTALS Charles W.

a neu menne u' man, I

N. Y., allincl- New York, N. Y., a corporation New York Application February 7, 1945, Serial No. 576.659

8 Gains. (Cl. 1315-188) This invention relates to electrical testing and more particularly to the testing of piezoelectric crystals to -be used in oscillators and in circuits.

In the copending application of Irvin E. Pair, Serial No. 574,953, nled January 27, 1945, now Patent No. 2,448,581, issued September '1, 1948, there is defined a new quality factor called the performance index" which is peculiar to piezoelectric crystals and of particular value in determining the quality and perfomance of such crys tals when used in oscillator circuits. 'I'he circuits and theory described therein are basically identical to those described in this application. Calibration difficulties were encountered, however, when attempts were made to measure the absolute value of the performance index of crystals which oscillate at the higher frequencies. It was discovered thatthese diiiiculties were due in part to the diiilculty in measuring with precision some of the small capacitances required in the test circuit and in part to the appearance of unavoidable stray reactances which became appreciably small at the` higher frequencies and which varied sufficiently from one test set to the analogous.

2 Le. Ref-Equivalent inductance and equivalent resistance of crystal, respectively. u==Test frequency multiplied by 2f.

In the above expression the perfomance index is arbitrarily defined as the ratio of the product of the equivalent inductive reactance of the crystal times the reactance of the external capacitance to the equivalent resistance of the crystal at the test frequency. Since both the equivalent crystal reactance and equivalent resistance are functions of frequency it is important that the test frequency be very accurately and precisely controlled in order to properly measure the performance index. It will be apparent that the performance index as thus dened takes into account several important fundamental parameters of the crystal. 'I'hese factors are particularly useful not only to indicate the crystal quality but the cause considerable error in the measured absolute values of the performance index. l

Since there are no primary standards available for the standardization or calibration of a performance index measuring instrument it necessarily follows that the instruments must be selfcalibrating by means of apparatus or circuits having circuit parameters of known magnitudes. At the higher frequencies some of these circuit parameters are very dimcult of accurate evaluation and it becomes necessary to determine the circuit constants by indirect means which means should be part of the internal calibrating ap' paratus of the test set.

The performance index was defined in the aforementioned copending application by the following expression:

where PI=Performance index. XLC=Equivalent inductive reactance of crystal at test frequency. Rc=Equivalent resistance of crystal at test frequency.

Xc2=Capacity reactance at ltest frequency of the external circuit capacitance C: Ain shunt with the crystal.

performance index is also design data.

It is the object of this invention to provide a self-callbrating circuit means for quickly and accurately measuring the performance index of a piezoelectric crystal. It is a further object of this invention to provide a self-calibrating means for a performance useful as important index measuring instrument which will correctly' take into account stray reactances in the measuring circuit as well as to take into account the effect of some of the small capacity reactances which are necessary parts of the test circuit but which are' difcult of precise evaluation by direct means.

The foregoing objects are attained 'by this invention by providing in combination with the crystal to be tested a source of alternating'current the frequency whereof is maintained equal to a predetermined operating frequency of the crystal under test. a capacity means for coupling the crystal to the source for driving the crystal, a series comprising a resistance means and second capacity means coupled to the driving circuit so as to have impressed thereon a voltage substantially proportional to the voltage appearing across the Afirst capacity means and a voltage measuring means connected across the second capacity means whereby the readings thereof will be a measure of the performance index of the crystal at the predetermined crystal operating frequency. A calibrating circuit is included as an integral part of the test setf'and comprises` a Calibrating capacitor and a calibrating' resistor connected-in series and to a source of alternating electric enersy, a iirst calibrating switching means for temporarily uncoupling from the rst capacity means aicaeie y the first-named series circuit comprising said resistance means and second capacity means and to selectively couple said first-named series circuit to either another part of said first capacity means or to the calibrating resistor per se, and a second calibrating switching means for temporarily short-circuiting the crystal under test.

The invention may be better understood by referring to the accompanyingdrawing in which:

Fig. 1A discloses the equivalent electrical network of a piezoelectric crystal;

Fig. 1B discloses the equivalent electrical network of the same crystal oscillating at a frequency between its resonant and antiresonant' frequencies in an oscillator circuit;

Fig. 2 is a circuit showing all the essential electrical circuit features of the invention;

Fig. 3 discloses the circuit set up in Fig. 2 with both calibratingswitches in the test position;

Figs. 4 and 5 are circuits set up in Fig. 2 during calibration, Fig. 4 disclosing the circuits set up when the switch Si is in its Test position and switch S2 is in the Cal 2 position, while Fig. 5 discloses the circuits set up in Fig. 2 whenswitch S1 is set to its Cal position while switch Sz may be set on either its Test position or its Cal 1 position;

Figs. 6 and 'It are explanatory of af shielding alternating current which may be an oscillator provides current to the test circuit through a automatic volume control and with its frequency feature employed in connection with switch Sg; Y

and

Fig. 8 discloses in greater detail the, oscillator circuit of Fig. 2.

Referring now to Fig. 1A the network I repre- I It should be noted that the network comprises a shunt capacitance Co connected in parallel with a series circuit comprising an inductance L1, resistance R1, and capacitance C1. 'It has been established that when a crystal is connected in an oscillator circuit it resonatessomewhere between its resonant and antiresonant frequencies, these frequencies actually being rather close together. that the impedance of a crystal `operating within this frequency range appears as a positive impedance or, more specifically, it appears as an inductive reactance in series with a resistance. This is shown in Fig. 1B in which the crystal network I is shown comprising a seriescircuit of Iinductance Lc and resistance Rc. This inductance and resistance are the equivalentv inductance and equivalent resistance `offthe crystall when connected to the oscillator circuit and operating at some frequency within the range above specified. crystal impedance may be expressed in the wellknown complex form as follows;

where f=oscillator or test frequency. l *i Moreover, it has also been established Under these conditions the.

lov

--put circuit of the'limiting amplifier 1.

under control of voltage derived from the crystal driving circuit. In this figure it will be noted that the frequency control voltage is derived from the drop across capacitor C1 which will be found in series with the crystal I, a variable capacitor Cs and the secondary winding S of the output transformer of the oscillator O. This voltage is fed back to the input circuit of the oscillator in proper phase to maintain oscillations at the oscillating frequency of the crystal whereby the source is automatically and rigidly maintained at the oscillating frequency of the crystal. This is a very important feature to the successful and convenient operation of this type of measuring equipment. Most any type of oscillator containing an automatic volume control and gain control means may be used in place of the particular arrangement shown' The only requirements are that the oscillator shall be of a type capable of being controlled in frequency by the crystal under test and that the voltage output of the oscillator must be under closely regulated automatic volume control as well as manual control of the output level. For these reasons the circuits as disclosed in block form in Fig. 2 are preferred. It will here be noted that the oscillator O comprises a limiting amplifier 1, a linear amplier 8, an output transformer comprising a primary P and secondary S tuned by a tuning condenser Cr and a feedback path from the crystal driving circuit to the input circuit of the limiting amplifier 1. The feedback path starts with the upper terminal of capacitor C'z through the left-hand terminal and'switch brush of switch SI and back to the in-v This oscillator also contains an automatic volume control rectifier, amplifier and gain control means I5 each component of which may be of conventional well-known design. It is preferred that the time constant of the limiting amplifier be different and preferably somewhat less than that of the auto- .matic volume control circuit in order to secure voltage stability.

Reference may be made to Fig. 8 for more detailed information of typical circuits which may be inserted in the various blocks of the oscillator of Fig. 2. Here it will be noted that the component circuits are of quite conventional form and need no special description. Briefly, however, it may be said that the limiting amplifier I The linear ampliiier 8 is also conventional.

is of a very old and well-known overloaded type. Its

,gain is a function of its control grid voltage bias,

a feature common to almost every automatic `volumecontrol amplierrcircuit. The automatic The basic features or the circuit as shown'rm Fig. 2 for measuring the performance index cfa piezoelectric crystal are substantially identical with those disclosed in the aforementioned copending application; This circuit in'addition shows the special features of thisy invention whichl` enable the apparatus to be accurately calibrated for the absolute measurement of the performance index of kcrystals operating in the higher fre-y quency ranges. It will be noted that the piezoelectric( crystal I is connected to the test set by means of test terminals 2 and 3. A source `of volume control circuit I5 is of the amplified backward-acting type, also well known in the art.

fthe diode circuit of the direct current amplifier tube, the diode being initially non-conducting.

The voltage output from linear amplifier 8 will be vrectified by the rectifier in circuit I5. As this vvoltage builds up it will produce an increasingly .rectified output across potentiometer 35 to increase the negative bias of the grid of the direct current amplifier tube. This in turn reduces the where the diode-anode becomes positive with respect to the cathode and current ows through the diode resistor 31 to rapidly increase the negative potential of the diode-anode to ground. Since this anode is connected directly to the control grid of amplifier 8, the bias on this grid is also increased rapidly to hold the oscillator output level at this point. The lever may be changed by adjusting control I' which changes the amount of rectified output voltage required to start the diode-current flowing. Potentiometer 35 adjusts the control range or control sensitivity of the circuit.

It is clearly obvious that while the particularcombination of circuits 1, 8 and I5 is new many other well-known equivalent component circuits may be substituted for those specifically disclosed to provide the same function.

Shielding is desirable around the crystaland the coupling capacitors Cs and C1. This may conform to well established principles and, for example, may take the preferred form specifically shown in Fig. 2 where a shield 29 is connected to test terminal 2 and interposed between the crystal and the rest of the test circuit. This acts to simulate an equipotential plane beneath the crystal so that capacitances between the crystal mounting structure connected to terminal 2 and ground will be in shunt with the secondary winding S while the capacitance which would exist between the crystal structure connected to terminal 3 and the rest of the test circuit is confined to a path in shunt with the crystal and hence is part of a capacitance Cx hereinafter more fully described.

Shield 30 surrounds variable capacitor Cc as shown to substantially eliminate the stray capacitance between the stator of capacitor Cc and ground which if permitted to exist would by-pass some of the current around capacitor C1.

Shield 3|, while it could be` dispensed with, is helpful in eliminating energy transfer between shields 29 and' 30.

A vacuum tube voltmeter MI may be connected across the terminals of the secondary winding S of the oscillator. The output voltage read by this meter is applied as a driving voltage to a series circuit comprising the piezoelectric crystal I and the two capacitors Cs and C1. By reason ofthe fact that this driving voltage read by the vacuum tube voltmeter MI is maintained rigorously constant by means of the automatic volume control circuit of the oscillator, it may be regarded as coming from a source of substantially zero impedance. Consequently, this driving voltage is eectively injected into the crystal branch of a parallel resonant network comprising the crystal network I shunted by the capacitance Cx and with the series-connected capacitors Cc and C1 eifectively connected in parallel with the crystal branch. The total external capacitance connected in parallel with the crystal I may, therefore, be expressed by the following equation:

the right-hand member of the equation are as Shown in Fig. 2. The capacitance Cx represents the unavoilable stray capacitance found across the terminals 2 and 3 of the test circuit and includes the capacitance added by shield 29. This capacitance is relatively small in magnitude, difficult of accurate evaluation and varies from one instrument to another. The existence of this capacitance, however, has been found to have an appreciable effect upon the accuracy of the absolute measurement of the performance index of crystals at relatively high frequencies. The calibrating features of this invention are directed to the problem of eliminating the effect of this stray capacitance and to thereby improve the a-ccuracy. In` the design of this portion of the circuit' the capacitance of capacitor Cr is made large compared with the capacitance of variable capacitor Ce. It will therefore be observed that inasmuch as capacitance Cx is also relatively small that the capacitance Cz connected in parallel with the crystal I is approximately equal to the capacitance of capacitor Cs. It will therefore be seen that the magnitude of the shunting capacitance can be varied by adjusting the capacitance of Cs. This is useful, as will be hereinafter more particularly described, in adjusting the shunt capacitance presented by the test set to thel crystal to equal the shunt capacitance presented to the crystal while in the commercial oscillator in which the crystal is ultimately to be used.

To aid in Calibrating the instrument a calibratl ing capacitor` CA is connected in series with a cali- In the above equation the capacitance Cz repy the test set. The various capacitances found in brating resistor RA and this series circuit is connected directly to the secondary winding S in the output circuit of the oscillator O. While other coupling means may be provided for connecting this calibrating circuit to the oscillator O, as for example that disclosed in the aforementioned copending application, the one here shown is very simple and is preferred for the calibrating scheme to be hereinafter more particularly described.

The frequency of theoscillator O may be determined hy connecting a frequency lindicator 4 to the output terminals. This frequency indicator 4 may comprise any well-known frequency indicator employing techniques well known in all laboratories engaged in high frequency measurements. One means suitable for determining this frequency is disclosed in United States Patent 2,283,616 issued May 19, 1942, to T. Slonczewski and F. R. Stansel.

The voltage drop appearing across capacitor C7 (which is part of the capacitance means coupling the crystal to the source of electrical energy) is applied to the input terminals of a pentode I0 through a capacity attenuator A. The schematic representation of this pentode I0 is conventional. The normalbias for the control grid is obtained by means of a conventional cathode resistor 22 by-passed by the by-pass capacitor 23. The suppressor grid is connected directly to the cathode and the screen grid to the source I2 through a resistor 20 and is by-passed to ground by means of a capacitor 2|. The plate is supplied from the direct current source I2 through the choke reactor I3 and plate resistor I9. The control grid is connected to ground through the grid resistor II. Connected in the output circuit of this tube is a variable capacitor Cp the reactance of which is preferably small compared with the alternating current plate resistance of the tube I0. Since the voltage er applied to the grid of tube Io is proportional to the voltage e1 appearing across capacitor C1 and since the resulting alternating voltage in the plate circuit of tube I is proportional to its grid voltage, the alternating voltage acting in the platecircut is always proportional to the voltage e'z. It is thus seen that the high plate resistance of tube I0 which is connected in series with capacitor CP is coupled to capacitor C1 which is part of the capacity means of the crystal driving circuit.

The vacuum tube voltmeter M2 may be of any type having a relatively high input impedance and is coupled to the capacitor Cp through the capacitor 24. By reason of the calibration circuits of this invention this meter need not be accurately calibrated but may have a purely arbitrary scale or even a single scale mark preferably from about one-half to full scale deflection.

Two switches Si and S2 are utilized in calibrating the apparatus for measuring the performance index of crystals. Switch S1 has two brushes, the left brush being connected directly to the input circuit of the limiting amplifier 1 of the oscillator O. In the Test position as shown in Fig. 2 this connects the input of the limiting ampliiler 1 directly to the capacitor C1 in the crystal driving circuit thereby causing the oscillator to be under control of the crystal for frequency stability. When the switch Si is moved to the calibrate position Cal the input circuit of the limiting amplifier 1 is connected to the secondary S of the output transformer in the oscillator. The reason for this change -in connection will be described later. The right-hand brush of switch S1 in the Test position makes no operative connection in the circuit.v However, in the calibrating position this brush places a short-circuit across the crystal i thereby also short-circuiting the stray capacitance Cx. In this position ofthe switch S1 the crystal I is no longer in the circuit of the oscillator so that this circuit is no longer resonant and consequently the voltage appearing across the capacitorA C1 reduces to a relatively low value. Since. in the test position, this voltage across the capacitor C7 is employed as the feedback voltage it will be obvious that when the switch S1 is moved to the calibrate position the feedback voltage would get very low if the feedback connection were not changed from across the capacitor C7 to directly across the output of the oscillator O. Therefore, -to maintain oscillations without having to introduce excessive gain in the oscillator circuit it is desirable to transfer the feedback circuit connection from across the capacitor C1 to directly across the output coil of the output transformer. The oscillator will not be expected to operate at the frequency of the crystal but at some other frequency. Since this calibrating position is, as

A hereinafter more fully described, merely used to obtain the ratio of voltages across two seriesconnected capacitors the actual frequency of the oscillator for this part of the calibration pro- `calibrate position the crystal is short-circuited and series-connected capacitors C@ and Cv are also connected directly across the generator. When switch Sz is moved to its Cal 2 position this same attenuator is again uncoupled from the crystal driving circuit and connected directly across the calibrating resistor RA. The lefthand switch brush of switch Sz as well as the connection from switch points 25 and 26 through conductor 21 to ground is for shielding purposes as will be more particularly described later in connection with Figs. 6 and '1. It can be shown that if the plate resistance Rz of pentode I0 is large compared with the reactance Xop it is not necessary that the calibrating network RA, CA be connected to a source having exactly the same frequency as the crystal. Thus a separate alternating current source may be used for all the calibration work. However, for economy of construction, simplicity of design and also for the sake of increased precision it is preferable that the same source used for driving the crystal also be used during calibration.

Due to the non-linear amplitude-frequency characteristic of some crystals and the non-linear amplitude-performance index characteristic of others, the voltage level at which the tests are made should be specified. This voltage level will usually be the voltage at which the crystal is ultimately expected to operate in the commercial oscillator. In order to aid in setting this voltage at the proper level a vacuum tube voltmeter M3 is temporarily connected across test terminals 2 and 3 as shown in Fig. 2. This meter is later f removed from the circuit before the actual measurement of the performance index is made and before the set is calibrated. The exact manner in which this meter M3 is used will be described in greater detail later.'

While some variation will obviously be possible in operating the above-described apparatus to measure the performance index of a crystal it is preferred that the following procedure be followed. With both switches Si and S2 in their Test positions the circuit will appear as shown in Fig. 3. Variable capacitor Cs should be adjusted until the total shunt capacitance presented by the test set to thecrystal is equal to that of the commercialoscillator. This total capacitance C2 is expressed by Equation 3 above. The value of this capacitance determines the exact frequency between the resonant and antiresonant points of the crystal at which the crystal will oscillate cedure is immaterial and has no effect upon the accuracy of the measurements.

'The other calibrating switch Si is shown to have three positions. The upper position is labeled Cai 1, the middle position Test and the lower position Cal 2. The use of these three positions will be described more fully later. At this point, however, it will be noted that when the switch S2 is moved to its upper calibrate position, denoted Cal 1, the attenuator A, and consequently the input circuit of the pentode I0 and meter circuit, is uncoupled from the crystal driving circuit and connected directly across the generator. Then when the switch S1 is also on its when in the commercial oscillator. It is therefore important that this capacitance be adjusted very accurately. It is preferable that the accuracy of this adjustment be observed by indirect means. Knowing the exact frequency at which the crystal I is expected to operate in the commercial oscillator the frequency indicator 4 is observed while capacitor Cs is varied. When capacitor Cs has been properly adjusted the frequency as indicated by the frequency indicator l will be exactly equal to the frequency at which the commercial oscillator is to operate and the shunting capacitance has been adjusted by Ce t0 be exactly equal to the capacitance which is to be presented by the commercial oscillator. This capacitance is mathematically defined for the test circuits by Equation 3 above.

Now with the Calibrating switches S1 and Sz still in their Test positions (Fig. 3) the capacitor Cr in the oscillator circuit should be adjusted until meter M2 reads its maximum deflection. This merely adjusts the tuned circuit T comprising aaeaeie the primary P of the output transformer of the l oscillator and its vtuning condenser Cr to resonate at the oscillating frequency of the crystal to be tested.

The test oscillator gain should be adjusted by adjusting the manual gain control dial Il until meter M3 connected across the crystals reads the voltage ec. This voltage may be defined as the required oscillating voltage which will appear .may be any value but preferably is arbitrarily made equal to unity. The circuits thus set up are shown in Fig. 4.' The calibrating voltage es across the calibrating circuit comprising capacitor CA and resistor RA, may be made any arbitrary value by changing the adjustment of the gain control. However, it isl convenient to leave this voltage eA equal to the inputtest voltage ei in order to simplify calculations. Ordinarily this condition 'will automatically obtain by reason of the automatic volume control function of the oscillator so that regardless of the operation of the switches S1 and Se this voltage will remain constant. In this position of the switches, that is,

with switch Si on its Test'position and switch Sz in its Cal 2 position. the capacitor Cr in the output circuit of pentode Ill (or alternatively, the gain of pentode I0) should be adjusted until meter M2 reads any convenient value from about onehalf to full scale deflection. 'I'his reading should be denoted es. It may here be stated that since voltage es may be of any arbitrary magnitude it may be derived from any alternating current source which is preferably, although not necessarily, of the same frequency as the crystal under test.

with switch s. sun in its 'rest position, switch S2 should be returned to its Test position so that the circuits of Fig. 3 will again obtain. If the gain control had been changed -as discussed in the preceding paragraph it should be readjusted until the test oscillator again produces the same output voltage e1 as read by meter MI in which case the voltage across the crystal will again be made substantially equal to the voltage ec. The

attenuator A should then be adjusted until meter r.

M2 reads a voltage er equal to the voltage ea previously obtained from the adjustments made while switch S2 was in its Cal 2 position. The attenuator reading should be read and this value denoted Ar. As the capacity attenuator A can be quite easily made to a high degree of precision this operation greatly relieves the stringent requirements on the linearity and accuracy with which the vacuum tube meter M2 must read.

With switch S2 remaining in its Test position move switch S1 to its calibrateposition Cal thereby setting up the circuits of Fig. 5. Then with the attenuator A set to equal Av (which is preferably made unity) adjust the capacitor CP until the meter M2 reads any convenient value from onehalf to full scale deflection. This reading of vacuum tube meter M2 may be denoted em'.

Referring again to Figs. 2 and 5, the switch Si should be left at its Cal position while switch Sz is moved to its Cal 1 position. In thesimpliiled circuits shown in Fig. 5 it is now assumed that the switch Se has been moved to its upper position. With this position of the switches the attenuator A should be readajusted until meter M2 again reads the'voltage em' previously determined. This position of theattenuator is denoted Az.

The performance index of the crystal under v pression Pl KA ,Af

test may now be calculated from the following exwhere and A-r and Az are attenuator readings obtained as specified above. l

That Equation 4 accurately expresses the absolute value of the performance index of the crystal where the apparatus is operated in the manner indicated above may be demonstrated by the following mathematical analysis. From Equation 1 the following expression may be written:

=J Lv. 1 & PI Rg ucl-w02 (5) Where L PL2.: (sa) InEquations 5 and 5a the quantity Qc is the Q of the crystal itself when oscillating at the required test,frequency. It is the ratioof the reactance to the resistance of the equivalent crystal network shown in Fig. 1B above. The effective circuit Q of the crystal including the stray capacitance Cx may be designatedQe, this quantity ex pressing the e'ective Q of the entire network actually appearing at the test terminals 2 and 3. lReferring to Fig. 3 it will be seen that Q may be expressed as follows remembering that the input capacitance of the attenator A is either made very small compared with the capacitance C1 or it is made substantially constant and included as part of the capacitance C1:

where voltages ei, et and e1 and capacitances Cs and C1 are as shown in Fig. 3.

The quantity Qs representing the Q of the entire network actually appearing at the test terminals may also be written as follows wherein the capacitance Cx is considered part of the crystal network as shown, for example, between the test terminals of Fig.

From the foregoing description of the circuits of this invention it will be remembered that the test frequency is automatically maintained under control of the crystal to equal the antiresonant frequency of the crystal when shunted by the external capacitance Cz. Consequently, thesum of the reactances in the crystal driving circuit around the series path from the driving voltage ei through the crystal network and through capacitors Cs and C1 must substantially equal zero. Therefore the following relationship obtains:

Qc; C1 fe'CT--cv (u) The performance index was expressed by Equation 5 in terms of the ratio of Qc to C: and the test frequency. From Equations 5 and 1l this may be written 61 C1 PI=2'w' C -2cx2 The voltage e1 will cause vacuum tube voltmeter M2 to respond in a manner governed by the intervening circuits. This relationship is derived in a conventional manner by considering the output circuit of the pentode i! as comprising a source of electromotive force of magnitude equal to the product of the amplification factor p of the tube and the alternating current grid voltage eg connected in series with the alternating current plate resistance R: of the tube and the capacitance Cp as shown schematically in Fig. 3. The grid voltage eg is expressed in terms of the voltage e1 across capacitor C1 and the attenuation factor A'r, which is the setting of the attenuator A when the test is being made with the switches in the positions shown in Fig. 3. This expression is:

e1=AT8l (13) The relationship in the output circuit of the tube I0 is expressed as:

e He|=XS #Raz-PXC,

where Substituting the value of e1 as defined by Equation 15 into Equation 12 will yield the following expression for the performance index:

All of the quantities in Equation 16 are constant, except Ar and ep. It is therefore apparent that if the constant quantities could be evaluated and if meter M2 were accurately calibrated, the instrument would be made direct reading, in which case the attenuator reading A'r would preferably be made equal to some multiple of ten and the performance index would be numerically equal to the reading of meter M2 or some multiple of ten thereof. However, the evaluation o! the performance index from Equation 16 has three obvious difficulties. First, the ratio of capacitance Cp to the mutual conductance Gm is diicult to evaluate numerically; second, the ratio of the two diierent voltages ep to ei is dimcult to get accurately if their absolute values must ilrst be obtained; third, the measurement is dependent upon the gain of the amplifier stage comprising tube il. All of these difilculties are overcome by the internal calibration circuits provided by this invention.

Now the ratio of the capacitance Cp to the mutual conductance Gm is evaluated by the calibration circuit of Fig. 4. The current through the calibrating network comprising calibrating capacitor CA and calibrating resistor RA (again neglecting the negligibly small current through the attenuator A) produces a total voltage drop of eA and a voltage drop of ea' across the calibrating resistor RA alone as shown in Fig. 4. 'I'his gives the following relations remembering that the resistance of RA is small compared with the reactance of the capacitor Ca.

GALUCA GAWCA 0 setting and the voltage across Cp during this part of the calibration procedure.

Solving Equation 17 for the voltage eA and substituting this value in Equation 18 will determine the ratio of the capacitance Cp to the mutual conductance Gm which ratio may be expressed as CAARA'. 1 GQ,l f Alea "/14- Xen): (19) @sie QARACL es e.' (G2-"C10z maar( 20) It will be remembered that in connection with the description of the operation of this apparatus the voltage eA during calibration is maintained equal to the input test voltage ei and since these voltages may both be read on the same meter MI and with the same scale factor the value of the performance index is entirely independent of the calibration of this meter. As a matter of fact the automatic volume control feature of the oscillator will actually keep these voltages equal without any special adjustment being necessary. It will also be remembered in connection with the description of the operation of this apparatus that when the switch S1 was in the Test position and the switch Sz in its Cal 2 position as shown in Fig. 4, the voltage en was determined. Then a 13 later with the two switches S1 and Sa in their test positions so that the circuits of Fig. 3 were set up the voltage ep was adjusted by adjusting the attenuator A until the voltage equals the voltage es. With these adjustments it will be ob vious that the voltage ratios appearing within the brackets in Equation' 20 above will reduce to unity and that the calibration of either meter MI or M2 is immaterial as they are always caused to read the same deilections. The accuracy with which the absolute value of the performance index may be determined therefore depends primarily upon the accuracy with which the capacity attenuator A is calibrated and the accuracy with which CA. RA, C1, Cz and Cx may be determined.

The variable capacity4 attenuator A may be calibrated to within a very small percentage error. The capacitance of C1 is relatively large, being in the order of 200 to 250 micromicrofarads and consequently can be accurately determined to within a fraction of a per cent error. While the capacitance CA is relatively small in a practical embodiment, the product of the capacitance CA times the resistance RA may be rather closely adjusted by adjusting the value of the resistance RA. 'I'he factor in the numerator of Equation 20, may be quite accurately determined by direct measurement without dimculty. For high frequency crystals, however, the capacitance Cx is not negligibly small compared with the external shunting capacitance Cz so that errors in their absolute determination will cause considerable error in the square of their difference. Accurate direct measurement of these capacitances is, as a practical matter, either impossible or at least extremely difilcult. However, by the additional intcrnal Calibrating means of this invention, this diillculty is easily overcome.

For this purpose switch Sris placed in the calibrate position Cal to temporarily short both the crystal and the stray capacitance Cx thereby setting up the circuit shown in Fig. 5. Switch S2 is first set to its Test position while the attenuator is arbitrarily set to read any value A1 whereupon the voltage across capacitor Cv is applied to the meter circuit to read a voltage em' on meter M2. Switch Sz is then set on its Cal 1 position whereupon the voltage across capacitors Cs and C7 in series is applied to the meter circuit. The attenuator is readjusted so meter Mz again reads em'. The new reading of the attenuator is designated A2. The effect of these adjustments may be analyzed as follows keeping in mind the test procedure vpreviously described.

With the circuits as'shown in Fig. 5 the input voltage applied to capacitors Ce and C7 in series is el' and the voltage across capacitor C1 alone is er'. Current through these capacitors is then equalto Solving Equation 21 for the ratio of elf to e1' and squaring We may write Substituting Equation 23 into Equation 22 will yield to the control grid of 'Alsoitistobe the accuracy of the 14 -Now meter M2l was made position of switch S: by adjusting' the attenuator A. Since the frequency is the same, voltage em' results in each case from a voltage em applied pentode I6. By reason of .the action of the attenuator, voltage el is equal to the product Azem and voltage e1' is equal to the product Aren.. The ratio of voltage el to e1' is therefore equal to the ratio of the attenuator readings Az to A1. Substituting this ratio in Equation 24' results-in Solving Equation 25 for the ratio of capacitance Cv to the square of the difference between the capacitance Cz and Cx and substituting in Equa tion 20 (remembering that the voltage ratios within the'brackets are made equal to unity) will yield CA R4 A2 PAAT-CT E) 26) As previously stated the product CARA and the capacitance C1 may be measured and adjusted to within very close limits. The ratio of the product of CARA to Cv is a design constant K which is preferably made equal to some multiple of 10. remembered that the attenuator may be adjusted during calibration so that its reading A1 may be equal to any arbitrary value within range. It is preferable for simplicity, however, to make this adjustment equal unity. Consequently Equation 26 reduces to Equation 4 and absolute calibration of the instrument is demonstrated as dependent only upon some very close approximations requiring that Qcyl, XcAsRA, and that C1Ce and also Aupon the accuracy with which the constant K 40 can be determined and the accuracy with which the attenuator A can be calibrated.` As previously stated capacity attenuators of this type can be calibrated to read consistently within very much closer limits than can vacuum tube voltmeters and the calibration is substantially independent of frequency.

Referring again to Fig. 2 where switch S2 is shown with two vbrushes the basic circuits of the invention may be set up -by the right-hand brush alone. It is also observed that except for the Test position the lefthand brush need not appear in the basic circuit schematic. 'I'his left-hand brush is used only as a capacity shielding means to eliminate the effect of a spurious switch capacitance which for a compactly constructed switch has been found at high frequencies to destroy the accuracy of the first calibration involving the standard capacitor and resistor CA and RA respectively. This shielding eil'ect is illustrated in Figs. 6 and 7 where the stray switch capacitance is designated Cs`and to read en' for each it is fully apparent that where it is assumed that switch Sz is in its Cal 2 position.

In Fig. 6

with switch points 25, 26 and 28 and switch point 2B is connected to test terminal 2 and switch point 26 is connected to the junction between standard capacitor CA and standard resistor RA. This assumption is made only to illustrate the -eiect of not utilizing the shielding connections disclosed in Fig. 2. With'such connections it is apparent that the stray capacitance Cs would couple switch point 28 connected to the junction of capacitors Cs and C1 with switch point 26 conit is further assumed that switch sa has only one brush, for example, the left brush nected to the upper stator of capacity attenuator A and to the junction between CA and RA. Now at resonance several volts appear as a drop across capacitor C1 while very much less voltage appears across the relatively low calibrating resistor RA which alone should be connected to the attenuator A as shown in Fig. 4. By reason of this stray coupling the voltage input to the attenuator A is raised somewhat above the calculated value thereby introducing an error in the calibration.

Fig. '7 shows the effect of using two brushes in the preferred manner as illustrated in Fig. 2. When switch Sz is in the Cal 2 position the small capacitance existing between switch point 28 and switch points 25 and 26 is connected across large capacitance C1 by conductor 21 where it is entirely harmless in its eiect. The only voltage now applied to the input side of the attenuator A is that appearing across the calibrating resistor RA just as intended.

What is claimed is:

1. A self-calibrating circuit for measuring the performance index of a piezoelectric crystal compri-sing a substantially zero output impedance source of alternating electric energy, a, crystal to be tested, a crystal driving circuit comprising two serially connected capacitors in series with the source and the crystal, one of said capacitors being large compared with the otherI a feedback circuit in said source connected to at least one of said capacitors whereby the frequency of the source is controlled by the crystal under test, a series circuit of a resistance means and a capacitive reactance means, the reactance whereof is small compared with the resistance, a coupling circuit for coupling said series circuit across the larger of said two capacitors so as to have impressed on said series circuit a voltage substantially proportional to the voltage across said larger capacitor, a voltage measuring means connected across said capacitive reactance whereby the readings thereof will be a measure of the performance index of the crystal and =a calibrating means therefor comprising a calibrating capacitor connected in series circuit with a calibrating resistor, a calibrating source of alternating electric energy connected across the last-named series circuit, a first switching means for temporarily disconnecting said coupling circuit from said larger capacitor and selectively reconnecting it across either the calibrating capacitor and calibrating resistor in series or the calibrating resistor alone, and a second switching means for temporarily short-circuiting the crystal.

2. A self-calibrating circuit for measuring the performance index of a piezoelectric crystal comprising a substantially zero output impedence source of alternating electric energy, a crystal to be tested, a crystal driving circuit comprising two serially connected capacitors in series with the source and the crystal, one of said capacitors being large compared with the other, a feedback circuit in said source connected to at least one of said capacitors whereby the frequency of the source is controlled by the crystal under test, a vacuum tube having input and output circuits, a capacitive reactance in series with the output circuit small compared to the resistance of said circuit. a circuit coupling the vacuum tube input circuit across the larger of said two capacitors, a voltage measuring means connected across said capacitive reactance whereby the reading thereof will be a measure of the performance index of the crystal, and a calibrating means therefor comprising a calibrating capacitor connected in 16 series circuit with a calibrating resistor, a. calibrating source of alternating electric energy connected across the last-named series circuit, a ilrst switching means for temporarily disconnecting the vacuum tube input circuit from said larger capacitor and selectively reconnecting it across either the calibrating capacitor and calibrating resistor in series, or the calibrating resistor alone, and a second switching means for temporarily short-circuiting the crystal.

3. A self-calibrating circuit for measuring the performance index of a piezoelectric crystal comprising a substantially zero output impedance source of alternating electric energy, a crystal to be tested, a crystal driving circuit comprising two serially connected capacitors in series with the source and the crystal, one of said capacitors being large compared with the other, a feedback circuit in said source connected to at lea'st one of said capacitors whereby the frequency of the source is controlled by the crystal under test, a series circuit of a resistance means and a capacitive reactance means, the reactance whereof is small compared with the resistance, a coupling circuit for coupling said series circuit across the larger of said two capacitors so as to have impressed on said series circuit a voltage substantially proportional to the voltage across said larger capacitor, a voltage measuring means connected across said capacitive reactance whereby the `readings thereof will be a measure of the performance index of the crystal, and a cali brating means therefor comprising a calibrating capacitor connected in series circuit with a calibrating resistor and across said source of electric energy, a first switching means for temporarily disconnecting said coupling circuit from said larger capacitor and selectively reconnecting it across either the calibrating capacitor and calibrating resistor in series, or the calibrating resistor alone, and a second switching means for temporarily short-circuiting the crystal.

4. A self-calibrating circuit for measuring the performance index of a piezoelectric crystal comprising a substantially zero output impedance source of alternating electric energy, a crystal to be tested, a crystal driving circuit comprising two serially connected capacitors in series with the source and the crystal, one of said capacitors being large compared with the other, a feedback circuit in said source connected to at least one of said capacitors whereby the frequency of the source is controlled by the crystal under test, a vacuum tube having input and output circuits, a capacitive reactance in series with the output circuit small compared to the resistance of said circuit, a circuit coupling the-vacuum tube input circuit across the larger of said two capacitors, a voltage measuring means connected icross said capacitive reactance whereby the readings thereof will be a measure of the performance index of the crystal, and a calibrating means therefor comprising a calibrating capacitor connected in series circuit with a calibrating resistor and across said source of electric energy, a first switching means for temporarily disconnecting the vacuum tube input circuit from said larger capacitor and selectively reconnecting it across either the calibrating capacitor and calibrating resistor in series, or the calibrating resistor alone, and a second switching means for temporarily short-circuiting the crystal.

5. The combination in accordance with claim l wherein said first switching means comprises a selector switch having at least three switch points 17 and a brush, a circuit connecting the brush to the coupling circuit, one circuit path from one of ,the switch points 'to the junction between said two serially connected capacitors, a second circuit path connecting a second switch point to one terminal of said Calibrating capacitor, and a third circuit path connecting a third switch point to lthe other terminal of said calibrating capacitor.

6. The combination in accordance with claim 2 wherein said rst switching means comprises a selector switch having at least three switch points and -a brush, a circuit connecting the brush to the" vacuum tube input circuit, one circuit path from lone of the switch points to the Junction between said two serially connected capacitors, a second circuit path connecting a second switch point to one terminal of said calibrating capacitor and a third circuit path connecting a third switch point to the other terminal o'f said calibrating capacitor.

7. The combination in accordance with claim 3 wherein said rst switching means comprises a selector switch having at least three switch points and a brush, a circuit connecting the brush to the coupling circuit, onecircuit path yfrom one oi' the switch points to the junction between said two serially connected capacitors, a second circuit .f 1s path connecting a second switch point to one terminal of said calibrating capacitor, and a third circuit path connecting a third switch point to the other terminal of said calibrating capacitor.

8. The combination in accordance with claim 4 wherein said .rst switching means comprises a selector switch having at least three switch points and a brush, a circuit connecting the brush to the vacuum tube input circuit, one circuit path from one of the switch points lto the junction between said two serially connected capacitors, a second circuit path connecting a second switch point to one terminal of said calibrating capacitor, and a third circuit ,path connecting a third switch point to the other terminal of said calibrating capacitor. ,i

CHARLES W. HARRISON.

REFERENCES crrEn The following references are of record in the file of this patent:

UNITED STATES PATENTS Loughlin Dec. 28, 1943 

